.. _sphx_glr_api_gallery_probability_classical:

Classical problems
-------------------

Buffon's needle and the St. Petersburg paradox.


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  <div id='sg-tag-list' class='sphx-glr-tag-list'></div>


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    <div class="sphx-glr-thumbnails">

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    <div class="sphx-glr-thumbcontainer" tooltip="A needle as long as the gap between parallel lines crosses a line with probability 2/\pi, so counting crossings estimates \pi. The estimate&#x27;s error shrinks like 1/\sqrt{n}.">

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  .. image:: /api/gallery/probability/classical/images/thumb/sphx_glr_plot_01_buffon_needle_thumb.png
    :alt:

  :doc:`/api/gallery/probability/classical/plot_01_buffon_needle`

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      <div class="sphx-glr-thumbnail-title">Buffon's needle: estimating pi by dropping needles</div>
    </div>


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    <div class="sphx-glr-thumbcontainer" tooltip="The game pays 2^k if the first head comes on toss k. Its expected payoff is infinite, so the running average of simulated payoffs never settles; it keeps jumping upward whenever a rare long run of tails occurs. Daniel Bernoulli&#x27;s logarithmic utility values the game at a small, finite amount.">

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  .. image:: /api/gallery/probability/classical/images/thumb/sphx_glr_plot_02_st_petersburg_paradox_thumb.png
    :alt:

  :doc:`/api/gallery/probability/classical/plot_02_st_petersburg_paradox`

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      <div class="sphx-glr-thumbnail-title">The St. Petersburg paradox</div>
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    </div>


.. toctree::
   :hidden:

   /api/gallery/probability/classical/plot_01_buffon_needle
   /api/gallery/probability/classical/plot_02_st_petersburg_paradox